A hybrid gene expression programming model for discharge prediction

Abstract

The head–discharge relationship of an overflow weir is a prerequisite for flow measurement. Conventionally, it is determined by regression methods. With machine learning techniques, data-driven modelling becomes an alternative. However, a standalone model may be inadequate to generate satisfactory results, particularly for a complex system. With the intention of improving the performance of standard gene expression programming (GEP), a hybrid evolutionary scheme is proposed, which is coupled with grey system theory and probabilistic technique. As a gene filter, grey relational analysis (GRA) eliminates noise and simulated annealing (SA) reduces overfitting by optimising the gene weights. The proposed GEP-based model was developed and validated using experimental data of a submerged pivot weir. Compared with standalone GEP, the GRA–GEP–SA model was found to generate more accurate results. Its coefficients of determination and correlation were improved by 3.6% and 1.7%, respectively. The root mean square error was lowered by 24.8%, which is significant. The number of datasets with an error of less than 10% and 20% was increased by 15% and 12%, respectively. The proposed approach outperforms classic genetic programming and shows a comparative error level with the empirical formula. The hybrid procedure also provides a reference for applications in other hydraulic issues.